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Permutations

Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders 123,132,213,231,312,321.

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Permutations -

Tag(s) : Combinatorics

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# Permutations

## Rank/Ordinal Number of a Permutation

Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders 123,132,213,231,312,321.

### What is a permutation? (Definition)

Item permutations consist in the list of all possible arrangements and ordering of elements in any order.

Example: The three letters A,B,C can be shuffled (anagrams) in 6 ways: A,B,C B,A,C C,A,B A,C,B B,C,A C,B,A

Permutations should not be confused with combinations (for which the order has no influence) or with arrangements also called partial permutations (k-permutations of some elements).

### How to generate permutations?

The best-known method is the Heap algorithm (method used by this dCode's calculator).

Step 1 - for each item, fix it at the beginning

Step 2 - repeat step 1 with the remaining items

Permutations can thus be represented as a tree of permutations: ### How to count permutations?

Counting permutations uses combinatorics and factorials

Example: For $n$ items, the number of permutations is equal to $n!$ (factorial of $n$)

### How to count distinct permutations?

Having a repeated item involves a division of the number of permutations by the number of permutations of these repeated items.

Example: DCODE 5 letters have $5! = 120$ permutations but contain the letter D twice (these $2$ letters D have $2!$ permutations), so divide the total number of permutations $5!$ by $2!$: $5!/2!=60$ distinct permutations.

### How to remove the limit when computing permutations?

Permutations makes exponential values which needs huge computing servers with huge memory cells, so the generation must be paid.

## Source code

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